Order and Disorder:
Classical and Romantic Physics in Arcadia

Mary Crone, Lublin Family Professor for Women in Science, Chemistry and Physics

A Fractal Image

Is life a series of conflicts between thinking and feeling, between order and disorder, between the Classical and the Romantic? Stoppard suggests that our interpersonal relationships and aesthetic preferences are driven by this dichotomy, and even goes so far as to suggest that our picture of the physical universe is, as well. In Arcadia, simple Newtonian physics represents Classicism. This "clockwork" view of the universe considers forces between a small number of objects in a controlled environment, and provides a metaphor for control, logic, and the picture of the world as orderly and unchanging. Two fields within physics represent Romanticism: the second law of thermodynamics, which was new in the nineteenth century; and chaos theory, which scientists and mathematicians have studied recently through the use of computers. These two fields are actually both outcomes of Newton's formulation of physics, and are therefore sometimes called "Classical" by physicists, although they represent Romanticism here. What makes these two fields different is that they deal with situations in the real world more complicated than a small number of objects in a controlled environment. In the case of thermodynamics, the difference is that a large number of objects are involved, like molecules in the air. In the case of chaos theory, the difference is that the system is very sensitive to small variations in the environment which we cannot predict. David Atkatz discusses chaos theory in the following essay, and I discuss the second law of thermodynamics in more detail here.

One way to summarize the second law of thermodynamics is to say that disorder increases. In this context, "disorder" has a specific technical definition which is often stated in terms of the temperature and energy of a system. In physics, this kind of disorder is called "entropy." A good simple way to think about entropy is randomness. For example, if you have 10 white balls and 10 yellow balls and you throw them into a box at random, it is likely that the colors will be pretty well mixed together, and unlikely that all the white balls will be at one end and all the yellow balls at the other. The reason the disordered state is more likely is simply a matter of statistics; there are many combinations of positions of the balls which look disordered, and only a few which look ordered. The second law of thermodynamics states that over time, systems tend to go into disordered states. If you start with many boxes of balls, some in ordered states, and other in disordered states, and shake them all around for a while, they will probably all look disordered in the end. In other words, entropy increases.

The second law sometimes seems puzzling because although is it mathematically consistent with Newton's laws for two bodies interacting, its implications are somewhat different. As summarized by Valentine, "... you can't run the film backward. Not like Newton." In other words, if you watch a movie of two balls colliding, there is no way of telling whether the movie is running backwards or forwards. On the other hand, if you watch a movie of many colored balls bouncing around, and it starts with all the yellow balls on one side and all the white balls on the other, and its ends with the colors mixed up, it is extremely likely that the move is running forwards rather than backwards.

Another reason the second law seems puzzling is that disorder does not always seem to increase; for example, we can pick up balls and put them in order. However, when we interact with the balls, we are making the situation more complicated. We expend energy to do this, our bodies produce heat which emanates out into the room, and this heat is an example of disorder! Think of the molecules in the air as balls and the temperature of the molecules as color. As the heat diffuses through the room, the temperature evens out, and entropy increases.

Finally, think about the implications of the second law when applied to all the atoms in the universe. Once again consider the color of the balls to indicate temperature. Then the implication is that the temperature at each location in the universe will eventually even out, although the eventual temperature might actually be something we would consider cold instead of hot! The point is that as the heat spreads out and entropy increases toward its maximum, what is left? Maybe maximum disorder means that nothing interesting ever happens again.

Thomasina remarks early in the play that disorder increases; she can stir jam and pudding together, but she cannot "stir them apart." More importantly, she realizes how profound this statement is --- that its implications go beyond the physics understood at her time. In the culminating scene, she makes the conceptual breakthrough that the performance of the heat engine illustrated by the "diagram" she is studying, is limited by the increase in entropy. In a heat engine, energy in the form of heat is converted to work (in this technical sense, "work" means forcing an object to move some distance). For example, heated steam may be used to expand and move a piston. Because heat is a more disordered form of energy than is work, the engine cannot convert heat to work with 100% efficiency without violating the second law of thermodynamics.

The role of physics in Arcadia is not only to illustrate Thomasina's genius, but to reflect the mentalities and the twists of fate in this story. As you read the play, notice how Stoppard uses thermodynamics to suggest that there is no "going back," and also how he uses chaos to suggest that people's lives are not simple and predictable. In the final scene, think about the double meaning of "heat death" and for Thomasina and Septimus: "Everything is mixing all the time, the same way, irreversibly... till there's no time left."

Mary Crone is an astrophysicist who studies the formation of galaxies and large-scale structure in the Universe. She earned her B.S. from the College of William & Mary and her Ph.D. from the University of Michigan. She has also done research at the Harvard-Smithsonian Center for Astrophysics, the University of Washington, and the University of Pittsburgh. She now holds the Charles Lubin Family Chair for Women in Science.